We study a (1 + 1)-dimensional field theory based on the ψ2ln2ψ2 potential which represents minimal nonlinearity in the context of phase transitions. There are three degenerate minima at ψ = 0 and ψ = ±1. There are novel, asymmetric kink solutions of the form ψ = ∓exp(−exp(±x)) connecting the minima at ψ = 0 and ψ = ∓1. The domains with ψ = 0 repel the linear excitations, the waves (e.g., phonons). Topology restricts the domain sequences and therefore the ordering of the domain walls. Collisions between domain walls are rich for properties such as transmission of kinks and particle conversion, etc. For illustrative purposes we provide a comparison of these results with the ϕ6 model and its half-kink solution, which has an exponential tail in contrast to the super-exponential tail for the ψ2ln2ψ2 potential. Finally, we place the results in the context of other logarithmic models.

中文翻译：

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最小非线性对数势：具有超指数分布的扭结

我们研究一个(1 + 1)维场论基于ψ2ln2ψ2势，表示相变环境中的最小非线性。有三个退化最小值ψ = 0和ψ = ±1. 有以下形式的新颖的不对称扭结解决方案ψ = ∓经验(-经验(±X))连接最小值ψ = 0和ψ = ∓1. 域与ψ = 0排斥线性激发，波（例如，声子）。拓扑限制了域序列，因此限制了域壁的排序。畴壁之间的碰撞具有丰富的属性，例如扭结的传输和粒子转换等。为了说明目的，我们将这些结果与φ6模型及其半扭结解，与ψ2ln2ψ2潜在的。最后，我们将结果放在其他对数模型的上下文中。